What is the closest star to our Sun that planets have been discovered orbiting?

Closest star to our Sun that has planets (yes earth-like) is Alpha Centauri B (about 4 and a half light years away).

Now the thing about earth-like extra solar planets is we don't know what the environment is like and we don't know if there is any life on it or not. All we can say is it's roughly earth sized (perhaps a bit bigger) and in the sweet zone of the star where it's thought liquid water could exist. That doesn't mean liquid water does exist there, Venus and Mars in our solar system would also qualify as earth-like, so remember when you read articles about earth-like or super earth planets discovered around other stars all that means is that they're rocky and in the sweet zone of a star.

Disclaimer:

The classification of Alpha Centauri Bb as an earth-like planet is not universally accepted, this exert from wikipedia gives more information about the controversial nature of the classification:

"On June 10, 2013, scientists reported that the earlier claims of an Earth-like exoplanet orbiting Alpha Centauri B may not be supported.[8] The existence of the planet remains a subject of scientific debate, and research by at least three separate groups of astronomers is ongoing."

I think many contributors have mus-understood your question.

At the moment (due to a new satellite) the discoveries are coming in thick and fast and you would be advised to check a website for the latest info.

I give just one for example. GOOGLE exo-planets

Alpha Centauri Bb but it's too close to it's "sun" to be habitable.

Beta Centauri b.

Yeah, there are plenty of stars close to our sun with planets. Some even very close and totally cool.